1. In a large Dutch oven, bring chicken stock to boil. Add chicken; cover and simmer over medium-low heat until juices run clear when chicken is pierced, about 30 minutes. With slotted spoon, transfer to plate; let cool. Remove meat from bones; cut into bite-size chunks.
2. Add carrots and potatoes to stock; cover and cook for 10 minutes. Add pearl onions; simmer, covered, just until onions are tender, about 5 minutes. With slotted spoon, transfer vegetables to plate. Pour stock into large measuring cup; if necessary, add more chicken stock to make 5 cups.
3. In same pan, melt butter/margarine over medium-high heat; cook celery, onion and mushrooms, stirring often, until softened, about 8 minutes. Add flour, thyme, salt and pepper; cook, stirring, for 1 minute. Gradually whisk in reserved stock; bring to boil, stirring. Reduce heat to medium-low; simmer, stirring often, for about 5 minutes or until thick enough to coat back of spoon. Return chicken and any accumulated juices to pan. Add carrot mixture, peas and cream, stirring to combine.

Dumplings:
In bowl, whisk together flour, parsley, baking powder and salt. Using pastry blender or 2 knives, cut in butter/margarine until coarse crumbs. Using fork, stir in enough milk to make sticky spoonable dough. Leaving space around each, drop by tablespoonfuls onto simmering stew; cover and cook, without lifting lid, for 20 minutes or until dumplings are no longer doughy underneath.